system size and beam energy dependence of azimuthal anisotropy from phenix michael issah vanderbilt...

System size and beam energy System size and beam energy dependence of azimuthal anisotropy dependence of azimuthal anisotropy

from PHENIXfrom PHENIX

Michael IssahVanderbilt University

for the PHENIX Collaboration

QM2008, Jaipur, India

QM 2008, Jaipur, India

2

Origin of azimuthal anisotropy

xx x

pyy

x x

py

x

pyy

x

Interactions among the produced particles lead to pressure gradients which generate an azimuthal anisotropy in particle emission or elliptic flow, measured by v2, from which can be obtained valuable information about the early dynamics after the collision

...)2cos2cos21(2

121

vv

d

dN

x

yz

x

yz

x

yz

x

yz

x

yz

x

yz

Spatial anisotropy Momentum anisotropy


3

Azimuthal anisotropy at different beam energies in Azimuthal anisotropy at different beam energies in Au+AuAu+Au collisionscollisions

Comparison between v2 for different pT and centralities show that the measured v2 is very similar at different beam energies Suggests that v2 does not change much with beam energy over the range √s=62.4-200 GeV

0-10%

10-20% 20-30% 30-40%


4

Centrality and pT dependence of elliptic flow at different

beam energies

Detailed differential centrality and pT dependence of v2 show similar magnitudes at √s = 62.4, 130 and 200 GeV Increase in measured v2 between SPS energies and RHIC energies

PRL 94, 232302 (2005)


5

Beam energy dependence of elliptic flowBeam energy dependence of elliptic flow

v2 saturates in the energy range √s=62.4-200 GeV suggesting a softening of the equation of state of matter at RHIC Extracted value for <cs> ≈ 0.35 ± 0.05 or <cs

2> ≈ 0.12 (PRL 98, 162301) This value lies between the ideal gas limit (cs

2=1/3) and mixed phase value (cs

2=0)

PRL 94, 232302 (2005)

F. Karsch, hep-lat/0601013


6

Beam energy comparison in Cu+CuBeam energy comparison in Cu+Cu

Measured v2 in Cu+Cu at √s = 62.4 GeV is observed to be of comparable magnitude or somewhat lower than v2 √s = 200 GeV. Systematic errors are big. The smaller size of the system and smaller energy densities created in Cu+Cu may be factors in explaining the difference observed in Cu+Cu compared Au+Au system

0-10% 10-20% 20-30% 30-40%


7

PRL. 98, 162301 (2007)

Hydrodynamic behavior tested by transverse kinetic energy scaling for low transverse kinetic energy KET = mT – m Baryon and mesons scale separately after KET ≥ 1 GeV Partonic recombination manifest by scaling by the number of constituent quarks nq (NCQ scaling) NCQ scaling is observed to break at around KET/nq ~1 GeV – see S. Huang’s talk later in the sesssion

Test of hydrodynamic behavior and partonic degrees of Test of hydrodynamic behavior and partonic degrees of freedom in Au+Au collisions at freedom in Au+Au collisions at √s = √s = 200 GeV200 GeV


8

Similar picture in Au+Au at 200 GeV and 62.4 GeV Partonic degrees of freedom are manifest in Au+Au collisions at √s=62.4 GeV

Au + Au at √s = 62.4 GeV


9

NCQ scaling NCQ scaling across systems and beam energies

Au+Au 200 GeV Cu+Cu 200 GeV Au+Au 62.4 GeV

PRL. 98, 162301 (2007)

Number of constituent quark scaling holds in Au+Au and Cu+Cu colliding systems at 200 GeV at low KET

Suggests that coalescence of particles with the quantum numbers of quarks occurs over the energy range 62.4 – 200 GeV for colliding systems of different sizes

Centrality 10-40%min bias


10

KET + Number of constituent Quarks (NCQ) scaling

Scaling seems to hold well for different centralities up to 60% centrality The goodness of the scaling can be tested by fitting the scaled curves with a polynomial and taking ratio of data/fit


11

Ratio of measured v2 to a fit to the data confirms that there is good NCQ scaling in the region where such scaling is expected to hold Scaling fails at low KET/nq (<0.2). Could be due to feed down from resonances More in-depth study of systematic errors needed at low KET as well as comparison to hydrodynamic models

NCQ scaling and fit to data


12

Reaction plane v2 less affected by non-flow than cumulant v2 because of large rapidity gap between PHENIX central arms and BBCs

Non-flow mainly due to jet correlations

Differences between reaction plane and cumulant v2 measurements show that jet correlations become influential as from pT ~3.5 GeV/c at all centralities

Non-flow contributions in Au+Au at Non-flow contributions in Au+Au at √s=200 GeV√s=200 GeV

PHENIXPreliminar

y


13

High statistics Run7 data enable detailed study of different flow harmonics

v4 of unidentified hadrons scale with integral flow between centrality 10-40%

v4/(ε’)2 is well described by (v2/ε’)2 up to pT ≈ 2 GeV/c

Ratio v4/v22 probes degree of thermalization

Results for different particle species reported in S. Huang’s talk later in this session

v4 of unidentified charged hadrons

A.TaranenkoPoster 212

ε’ : <v2>


14

SummarySummary Differential azimuthal anisotropy measurements in Au+Au and

Cu+Cu at different beam energies and centralities indicate saturation of v2 with beam energy at RHIC

Transverse kinetic energy (KET) scaling, as well as number of constituent quark scaling, is observed in both systems at different beam energies and for KET/nq < 1 GeV and for centrality up to 60%

More in depth study needed to look into the goodness of the KET/nq scaling at low KET

Comparison between reaction plane and cumulant v2 shows

that non-flow correlations due to jet correlations exist for different centralities as from pT ~3.0 – 4.0 GeV/c. May explain the break of the NCQ scaling at KET > 1 GeV

Detailed study of different flow harmonics carried out in Run7. It is observed that v4 scales with eccentricity and with v2

2


15

Thanks to: M. Shimomoura, H. Masui and A. Taranenko

Acknowledgements


16

BACK UP


17

Eccentricity scaling across colliding systemsEccentricity scaling across colliding systems

k ~ 3.1 (from data )

Eccentricity scaling observed in hydrodynamic model over a broad range of centralities v2 is observed to scale with eccentricity and across system size

Hydrodynamic model simulations (Bhalerao,

Blaizot, Borghini, Ollitrault , nucl-th/0508009)


18

Estimate of the speed of soundEstimate of the speed of sound (I)(I)

Energy dependence at RHIC energies seem to indicate a soft equation of state. How soft ?

Estimate of cs from elliptic flow measurements can be made from

eccentricity scaled v2

Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009


19

Eccentricity scaling from PHOBOS

system size and beam energy dependence of azimuthal anisotropy from phenix michael issah vanderbilt...

Documents